The invention relates to a reamer for the fine machining of a bore. The reamer according to the invention is used for the fine machining of bores having varying bore cross-sections. In particular, the reamer is suitable for the machining of cartridge chambers of firearms. Such cartridge chambers are produced from the solid. The cartridge chamber precedes the weapon barrel, and has a stepped drilled hole having a front portion having a smaller region that matches the shape of the tip of the cartridge and, adjoining said region, a cylindrical region of greater diameter. According to the prior art, the drilled holes drilled from the solid are fine machined by means of reamers. According to the prior art, this machining takes approximately 3 minutes per cartridge chamber.
Preceding therefrom, the invention is based on the object of reducing the machining time.